Electron Propagator Theory

Orbitals and the Interpretation of Photoelectron Spectroscopy and (e,2e) Ionization Experiments

“…In principle,the Dyson orbital could be obtained directly from Dysonsi ntegral equations involving the self-ener-gy, [42][43][44] but in quantum chemistry it is usually calculated (approximated) from the definition in Equation (2). Forbest accuracy,D yson orbitals should be calculated from fully correlated wave functions,b ut it is informative to consider calculating them in the HF approximation, which one might hope to give ag ood approximation for weakly correlated molecules.Ifone uses the HF approximation for Y N and Y NÀ1 and one makes the approximations described above leading to Koopmans theorem, then the Dyson orbital becomes ac anonical HF orbital, and comparisons of canonical HF orbitals to Dyson orbitals have shown this to be ag ood approximation for some simple molecules.…”

“…In principle, the Dyson orbital could be obtained directly from Dyson's integral equations involving the self‐energy, but in quantum chemistry it is usually calculated (approximated) from the definition in Equation (2). For best accuracy, Dyson orbitals should be calculated from fully correlated wave functions, but it is informative to consider calculating them in the HF approximation, which one might hope to give a good approximation for weakly correlated molecules.…”

The any particle molecular orbital approach: A short review of the theory and applications

“…The Møller–Plesset many body perturbation theory has been applied to the APMO‐HF Refs . It is convenient to present these equations in a MC second quantization formalism.…”

“…This equation can be expressed as the inverse form of the Dyson equation where the self‐energy matrix for an α particle, Σ α , accounts for correlation and relaxation effects missing in the zero order propagator. The off‐diagonal elements of Σ are regularly neglected in applications of the theory to ionization processes, such as valence electron ionization . In such cases, the above equation is reduced to a simpler form of the Dyson Equation , known as the quasiparticle (diagonal) approximation …”

Communication: Explicitly correlated formalism for second-order single-particle Green’s function

“…Whereas GF formalism is dominant in condensed phase physics as a step beyond the mean-field description, it has also enjoyed a sustained, albeit a less prominent, presence in the molecular electronic structure. 2,3 The single-particle GF, or electron propagator, has primarily been employed as a computationally efficient route to post-mean-field ionization potentials (IP) and electron affinities (EA) and, more generally, spectral functions necessary to interpret various photoelectron spectroscopies; recently self-consistent GF theory has been revisited as a route to quantum embedding and to finite-temperature electronic structure. 4,5 Here we present a general, explicitly correlated formalism for computing single-particle Green's functions.…”